The integration in the above expression can be treated with solving the saddle-point equation [1]}, [2]}
\(\begin{aligned}&[\textbf {p}_{st}+\textbf {A}(t^{\prime }_{s})]^{2}/2+I_{p}=0;\\&[\textbf {p}_{st}+\textbf {A}(t_{s})]^{2}/2+I_{p}=\omega .\end{aligned}\) 
